Question

chứng minh rằng 10^9 + 8  chia hết cho 72

mn giúp mik nhanh vs nha! thank

 

Answer 1

Ta có: \(10^9=10^3.10^6=1000.10^6\)

Vì \(1000⋮8\)\(\Rightarrow1000.10^6⋮8\)\(\Rightarrow10^9⋮8\)

mà \(8⋮8\)\(\Rightarrow10^9+8⋮8\)

Ta có: \(10^9+8=100....0+8=100.....08\)

Vì \(1+0+0+...+0+8=9⋮9\)\(\Rightarrow10^9+8⋮9\)

mà \(\left(8;9\right)=1\)\(\Rightarrow10^9+8⋮8.9\)\(\Rightarrow10^9+8⋮72\)( đpcm )